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|Title:||The use of nonnull models for ranks in nonparametric statistics|
|Doctoral Committee Chair(s):||Marden, John I.|
|Department / Program:||Statistics|
|Degree Granting Institution:||University of Illinois at Urbana-Champaign|
|Abstract:||A popular nonparametric measure of a monotone relation between two variables is Kendall's tau. Originally, most analysis of this statistic assumed the two variables were independent, while more recently there has been interest in finding "nonnull" models for the observations which allow types of dependence. One such model popularized by Mallows (1957, Annals of Mathematical Statistics) uses a one-parameter exponential family model with the canonical sufficient statistic being equivalent to Kendall's tau.
This thesis explores theoretical and practical aspects of this model. Asymptotic normality of the statistic is proved, and good asymptotic approximations for its mean and variance are found. It is shown that the Maximum Likelihood Estimator of the parameter is asymptotically normal. These results are obtained for the case with neither variable having any ties and for the case with one variable being an indicator variable, in which case the statistic becomes the Mann-Whitney statistic for comparing two groups. Some extensions are made to comparing several groups.
In order to understand how well the model works in practice, its performance is evaluated under various bivariate and location-family models. It appears to be a good proxy for many models.
|Rights Information:||Copyright 1989 Chung, Lyinn|
|Date Available in IDEALS:||2011-05-07|
|Identifier in Online Catalog:||AAI9010832|